|
Refutation Table
{{no footnotes, date=November 2017 A transposition table is a cache of previously seen positions, and associated evaluations, in a game tree generated by a computer game playing program. If a position recurs via a different sequence of moves, the value of the position is retrieved from the table, avoiding re-searching the game tree below that position. Transposition tables are primarily useful in perfect-information games (where the entire state of the game is known to all players at all times). The usage of transposition tables is essentially memoization applied to the tree search and is a form of dynamic programming. Transposition tables are typically implemented as hash tables encoding the current board position as the hash index. The number of possible positions that may occur in a game tree is an exponential function of depth of search, and can be thousands to millions or even much greater. Transposition tables may therefore consume most of available system memory and ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect-information Game
Perfect information is a concept in game theory and economics that describes a situation where all players in a game or all participants in a market have knowledge of all relevant information in the system. This is different than complete information, which implies common knowledge of each agent's utility functions, payoffs, strategies and "types". A system with perfect information may or may not have complete information. In economics this is sometimes described as "no hidden information" and is a feature of perfect competition. In a market with perfect information all consumers and producers would have complete and instantaneous knowledge of all market prices, their own utility and cost functions. In game theory, a sequential game has perfect information if each player, when making any decision, is perfectly informed of all the events that have previously occurred, including the "initialization event" of the game (e.g. the starting hands of each player in a card game).Archived a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Deepening Depth-first Search
In computer science, iterative deepening search or more specifically iterative deepening depth-first search (IDS or IDDFS) is a state space/graph search strategy in which a depth-limited version of depth-first search is run repeatedly with increasing depth limits until the goal is found. IDDFS is optimal, meaning that it finds the shallowest goal. Since it visits all the nodes in the search tree down to depth d before visiting any nodes at depth d + 1, the cumulative order in which nodes are first visited is effectively the same as in breadth-first search. However, IDDFS uses much less memory. Algorithm for directed graphs The following pseudocode shows IDDFS implemented in terms of a recursive depth-limited DFS (called DLS) for directed graphs. This implementation of IDDFS does not account for already-visited nodes. function IDDFS(root) is for depth from 0 to ∞ do found, remaining ← DLS(root, depth) if found ≠ null then return found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alpha-beta Pruning
Alphabeta or Alpha Beta may also refer to: * Alphabeta, an Israeli musical group * Alpha Beta, a former chain of Californian supermarkets * The Greek alphabet, from ''Alpha'' (Αα) and ''Beta'' (Ββ), the first two letters * Alpha and beta anomers (chemistry) * Alpha–beta pruning, a type of search algorithm * Alpha–beta transformation, a mathematical transformation in electrical engineering * α,β-Unsaturated carbonyl compound, a class of organic compounds * Alpha beta filter, a predictive filter * Alpha (finance) and Beta (finance) In finance, the beta ( or market beta or beta coefficient) is a statistic that measures the expected increase or decrease of an individual stock price in proportion to movements of the stock market as a whole. Beta can be used to indicate the c ..., two measures characterizing the return of an investment portfolio * The Alpha Betas, a fraternity in the '' Revenge of the Nerds'' film series * ''Alpha Betas,'' an animated webseries created by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimax Algorithm
Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for ''minimizing'' the possible loss function, loss for a Worst-case scenario, worst case (''max''imum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of uncertainty. Game theory In general games The maximin value is the highest value that the player can be sure to get without knowing the actions of the other players; equivalently, it is the lowest value the other players can force the player to receive when they know the player's action. Its formal definition is: :\underline = \max_ \min_ W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Variation
A variation can refer to a specific sequence of successive moves in a turn-based game, often used to specify a hypothetical future state of a game that is being played. Although the term is most commonly used in the context of Chess analysis, it has been applied to other games. It also is a useful term used when describing computer tree-search algorithms (for example minimax) for playing games such as Go{{cite web , url=http://www.andromeda.com/people/ddyer/go/search.html, title=Searches, tree pruning and tree ordering in Go, date=21 December 2007 or Chess. A variation can be any number of steps as long as each step would be legal if it were to be played. It is often as far ahead as a human or computer can calculate; or however long is necessary to reach a particular position of interest. It may also lead to a terminal state in the game, in which case the term "winning variation" or "losing variation" is sometimes used. Principal variation The principal variation refers to the pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cache (computing)
In computing, a cache ( ) is a hardware or software component that stores data so that future requests for that data can be served faster; the data stored in a cache might be the result of an earlier computation or a copy of data stored elsewhere. A cache hit occurs when the requested data can be found in a cache, while a cache miss occurs when it cannot. Cache hits are served by reading data from the cache, which is faster than recomputing a result or reading from a slower data store; thus, the more requests that can be served from the cache, the faster the system performs. To be cost-effective, caches must be relatively small. Nevertheless, caches are effective in many areas of computing because typical Application software, computer applications access data with a high degree of locality of reference. Such access patterns exhibit temporal locality, where data is requested that has been recently requested, and spatial locality, where data is requested that is stored near dat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pawn (chess)
The pawn (♙, ♟) is the most numerous and weakest piece in the game of chess. It may move one square directly forward, it may move two squares directly forward on its first move, and it may capture one square diagonally forward. Each player begins a game with eight pawns, one on each square of their second . The white pawns start on a2 through h2; the black pawns start on a7 through h7. Individual pawns are referred to by the on which they stand. For example, one speaks of "White's f-pawn" or "Black's b-pawn". Alternatively, they can be referred to by the piece which stood on that file at the beginning of the game, e.g. "White's king bishop's pawn" or "Black's queen knight's pawn". It is also common to refer to a ''rook's pawn'', meaning any pawn on the a- or h-files, a ''knight's pawn'' (on the b- or g-files), a ''bishop's pawn'' (on the c- or f-files), a ''queen's pawn'' (on the d-file), a ''king's pawn'' (on the e-file), and a ''central pawn'' (on the d- or e-files). The p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Threefold Repetition
In chess, the threefold repetition rule states that a player may claim a draw if the same position occurs three times during the game. The rule is also known as repetition of position and, in the USCF rules, as triple occurrence of position.Article 14K.2 in Two positions are by definition "the same" if pieces of the same type and color occupy the same squares, the same player has the move, the remaining castling rights are the same and the possibility to capture ''en passant'' is the same. The repeated positions need not occur in succession. The game is not automatically drawn if a position occurs for the third time – one of the players, on their turn, must claim the draw with the arbiter. The claim must be made either before making the move which will produce the third repetition, or after the opponent has made a move producing a third repetition. By contrast, the fivefold repetition rule requires the arbiter to intervene and declare the game drawn if the same position occurs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zobrist Hashing
Zobrist hashing (also referred to as Zobrist keys or Zobrist signatures Bruce Moreland/ref>) is a hash function construction used in computer programs that play abstract board games, such as chess and Go, to implement transposition tables, a special kind of hash table that is indexed by a board position and used to avoid analyzing the same position more than once. Zobrist hashing is named for its inventor, Albert Lindsey Zobrist. It has also been applied as a method for recognizing substitutional alloy configurations in simulations of crystalline materials. Zobrist hashing is the first known instance of the generally useful underlying technique called tabulation hashing. Calculation of the hash value Zobrist hashing starts by randomly generating bitstrings for each possible element of a board game, i.e. for each combination of a piece and a position (in the game of chess, that's 6 pieces × 2 colors × 64 board positions, with a constant number of additional bitstrings for ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alpha–beta Pruning
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the Minimax#Minimax algorithm with alternate moves, minimax algorithm in its game tree, search tree. It is an adversarial search algorithm used commonly for machine playing of two-player Combinatorial game theory, combinatorial games (Tic-tac-toe, Chess, Connect 4, etc.). It stops evaluating a move when at least one possibility has been found that proves the move to be worse than a previously examined move. Such moves need not be evaluated further. When applied to a standard minimax tree, it returns the same move as minimax would, but prunes away branches that cannot possibly influence the final decision. History John McCarthy during the Dartmouth workshop, Dartmouth Workshop met Alex Bernstein of IBM, who was writing a chess program. McCarthy invented alpha–beta search and recommended it to him, but Bernstein was "unconvinced". Allen Newell and Herbert A. Simon who us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memoization
In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls to pure functions and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing. It is a type of caching, distinct from other forms of caching such as buffering and page replacement. In the context of some logic programming languages, memoization is also known as tabling. Etymology The term ''memoization'' was coined by Donald Michie in 1968 and is derived from the Latin word ('to be remembered'), usually truncated as ''memo'' in American English, and thus carries the meaning of 'turning he results ofa function into something to be remembered'. While ''memoization'' might be confused with ''memorization'' (because they are etymological cognates), ''memoization'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cache (computing)
In computing, a cache ( ) is a hardware or software component that stores data so that future requests for that data can be served faster; the data stored in a cache might be the result of an earlier computation or a copy of data stored elsewhere. A cache hit occurs when the requested data can be found in a cache, while a cache miss occurs when it cannot. Cache hits are served by reading data from the cache, which is faster than recomputing a result or reading from a slower data store; thus, the more requests that can be served from the cache, the faster the system performs. To be cost-effective, caches must be relatively small. Nevertheless, caches are effective in many areas of computing because typical Application software, computer applications access data with a high degree of locality of reference. Such access patterns exhibit temporal locality, where data is requested that has been recently requested, and spatial locality, where data is requested that is stored near dat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
